相关论文: Singular Reduction of the 2-Body Problem on the 3-…

Observing the list of compatible second order equations of Absolute Parallelism (AP) found by Einstein and Mayer (they used D=4), we choose the one-parameter class of equations which take on a 3-linear form (when contra-frame density of…

Mitchell and Littlejohn showed that isotropy groups and orbits for $N$-body problems attain a sense of genericity for $N = 5$. The author recently showed that the arbitrary-$d$ generalization of this 3-$d$ result is that genericity in this…

The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations…

Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems…

The automorphisms of a two-generator free group acting on the space of orientation-preserving isometric actions of on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on…

It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…

With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so…

We consider solutions of the 2x2 matrix Hamiltonians of the physical systems within the context of the su(2) and su(1,1) Lie algebra. Our technique is relatively simple when compared with the others and treats those Hamiltonians which can…

The symplectomorphism group of a 2-dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition…

This is the second of two companion papers. We describe a generalization of the point vortex system on surfaces to a Hamiltonian dynamical system consisting of two or three points on complex projective space CP^2 interacting via a…

Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the…

We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally…

We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and…

We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for…

This paper studies the reduction by symmetry of a variational obstacle avoidance problem. We derive the reduced necessary conditions in the case of Lie groups endowed with a left-invariant metric, and for its corresponding Riemannian…

A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…

We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…

A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…

In this paper we describe optimal reduction for the system of two bodies in $\mathbb{R}^3$ whose Hamiltonian is invariant under rotations and translations. In doing this, we introduce parametrizations and charts which help giving explicit…

We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we…